Diesel aircraft engines and are the light jets pushing out the twins?

I don't see the fuel burn on the small turbines competing with the diesels,
but there are some attempts at getting close to the Lycosaur level.

Here is one - http://www.innodyn.com/

Don't know anything about them though.

As for light jets pushing down demand for twin piston and turbo props, you
are correct. You mentioned Diamond, and they are going straight after the
light twin and turbine single engine market with their single engine jet.
If you will accept a single engine, the economics seem to make sense to go
that route rather than with an equally expensive Piper or Beech plane.

It will be interesting to see what will happen. Some missions will likely
push folks to stick with the prop planes though.